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Abstract

The article describes optimization of the process of acceleration of the tower crane trolley movement mechanism during the steady mode of the slewing mechanism. A mathematical model of the boom system of the tower crane was used for the optimization of the trolley movement. The model was reduced to a sixth-order linear differential equation with constant coefficients, which represents the relationships between the drive torque and the coordinate of the load and its time derivatives. Non-dimensional complex criterion (objective function), which takes into account the drive torque and its rate of change in time during the transient process, was developed to optimize the mode of the trolley movement mechanism. Based on that, a variational problem was formulated and solved in an analytical form in which root-mean-square (RMS) values of the quantiles were applied. A complex optimal mode of acceleration of the trolley movement mechanism was obtained and compared with the modes optimized based on different criteria. Advantages and disadvantages of the solutions were discussed based on the analysis of the obtained optimal modes of motion. The analysis revealed low- and high-frequency elements oscillations of the trolley movement mechanism during the transient processes. The conditions for their elimination were formulated.
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Bibliography

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[9] S.-J. Kimmerle, M. Gerdts, and R. Herzog. Optimal control of an elastic crane-trolley-load system – a case study for optimal control of coupled ODE-PDE systems – (extended version with two appendices). Mathematical and Computer Modelling of Dynamical Systems, 24(2):182–206, 2018. doi: 10.1080/13873954.2017.1405046.
[10] V. Loveikin, Y. Romasevych, I. Kadykalo, and A. Liashko. Optimization of the swinging mode of the boom crane upon a complex integral criterion. Journal of Theoretical and Applied Mechanics, 49(3):285–296, 2019. doi: 10.7546/JTAM.49.19.03.07.
[11] Z. Liu, T. Yang, N. Sun, and Y. Fang. An antiswing trajectory planning method with state constraints for 4-DOF tower cranes: design and experiments. IEEE Access, 7:62142–62151, 2019. doi: 10.1109/ACCESS.2019.2915999.
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[14] K.W. Cassel. Variational Methods with Applications in Science and Engineering. Cambridge University Press, 2013. doi: 10.1017/CBO9781139136860.
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Authors and Affiliations

Viatcheslav Loveikin
1
Yuriy Romasevych
1
ORCID: ORCID
Andriy Loveikin
2
Mykola Korobko
1
ORCID: ORCID

  1. National University of Life and Environmental Sciences of Ukraine, Kyiv, Ukraine
  2. Taras Shevchenko National University of Kyiv, Ukraine
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Abstract

In the present study, the problem of optimization of the motion mode of the tower crane's slewing mechanism in the steady-state mode of trolley movement is stated and solved. An optimization criterion, which includes the RMS values of the drive torque and the rate of its change over time, is minimized. The optimization is carried out taking into account the drive torque constraints, and under the specified boundary conditions of motion. Three optimization problems at different values of the weight coefficients are solved. In the first problem, priority is given to the drive torque, in the third – to the rate of the drive torque change, and in the second problem, the significance of both components is assumed equal. The optimization problems are nonlinear, thus a VСT-PSO method is applied to solve them. The obtained optimal start-up modes of the crane slewing mechanism eliminate pendulum load oscillations and high-frequency elastic oscillations of the tower. Most of the kinematic, dynamical, and power parameters at different values of the weight coefficients are quite close to each other. It indicates that the optimal modes of motion are significantly influenced by the boundary conditions, optimization parameters, and constraints
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Bibliography

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[6] V. Loveikin, Yu. Romasevych, A. Loveikin, and M. Korobko. Optimization of the trolley mechanism acceleration during tower crane steady slewing. Archive of Mechanical Engineering, 69(3):411–429, 2022. doi: 10.24425/ame.2022.140424.
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[13] S. Chwastek. Optimization of crane mechanism to reduce vibration. Automation in Construction, 119:103335, 2020. doi: 10.1016/j.autcon.2020.103335.
[14] V. Loveikin, Yu. Romasevych, A. Loveikin, A. Lyashko,and M. Korobko. Minimization of high frequency oscillations of trolley movement mechanism during steady tower crane slewing. UPB Scientific Bulletin, Series D: Mechanical Engineering, 84(1):31-44, 2022.
[15] Z. Liu, T. Yang, N. Sun, and Y. Fang. An antiswing trajectory planning method with state constraints for 4-DOF tower cranes: Design and experiments. IEEE Access, 7: 62142–62151, 2019. doi: 10.1109/ACCESS.2019.2915999.
[16] T.K. Nguyen. Combination of feedback control and spring-damper to reduce the vibration of crane payload. Archive of Mechanical Engineering, 68(2):165–181, 2021. doi: 10.24425/ame.2021.137046.
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[19] S.-J. Kimmerle, M. Gerdts, and R. Herzog. An optimal control problem for a rotating elastic crane-trolley-load system. IFAC-PapersOnLine, 51(2):272-277, 2018, doi: 10.1016/j.ifacol.2018.03.047.
[20] Y. Romasevych, V. Loveikin, and Y. Loveikin. Development of a PSO modification with varying cognitive term. 2022 IEEE 3rd KhPI Week on Advanced Technology, KhPI Week 2022 – Conference Proceedings, Kharkiv, Ukraine, 2022. doi: 10.1109/KhPIWeek57572.2022.9916413.
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Authors and Affiliations

Viacheslav Loveikin
1
ORCID: ORCID
Yuriy Romasevych
1
ORCID: ORCID
Andrii Loveilin
2
ORCID: ORCID
Mykola Korobko
1
ORCID: ORCID
Anastasia Liashko
1
ORCID: ORCID

  1. National University of Life and Environmental Sciences of Ukraine, Kyiv, Ukraine
  2. Taras Shevchenko National University of Kyiv, Ukraine

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